Uruguayan centre-half Diego Godin got the winner for Atletico on 40 minutes stabbing the ball home from two yards out after a scramble in the box following a corner.
Atletico had goalkeeper Thibaut Courtois, on loan from Chelsea, to thank for the three points after he made a number of fine saves, most notably an acrobatic block from Raul Garcia's header on 75 minutes.
The result means Atletico have taken 10 points from four games since ex-club legend Simeone took over during the Christmas break, without conceding a goal.
The three points moves the team from the capital above Osasuna into seventh position, level on points with sixth placed Athletic Bilbao who currently hold the last place that guarantees qualification to next season's Europa League.
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